research operation

7/24/2019 research operation

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Gudang 1 2 3 kapasitas

1 100 100 120 150

2 120 100 100 450

3 100 110 120 300

4 100 110 120 300

Demand 400 400 400 1200

formulasi

1. identikasi variabel

X1,1ban!akn!a barang dikirim dari gudang 1 ke pasar 1

"1,2ban!akn!a barang dikirim dari gudang 1 ke pasar 2











2.#dentikasi kendala $tandarisasi %anonikal

"1,1&"1,2&"1,3'150 "1,1&"1,2&"1,3&"a150

"2,1&"2,2&"2,3'450 "2,1&"2,2&"2,3&"b450

"3,1&"3,2&"3,3'300 "3,1&"3,2&"3,3&"(300

"4,1&"4,2&"4,3'300 "4,1&"4,2&"4,3&"d300

"1,1&"2,1&"3,1&"4,1)400 "1,1&"2,1&"3,1&"4,1*"e400

"1,2&"2,2&"3,2&"4,2)400 "1,2&"2,2&"3,2&"4,2*"f400

"1,3&"2,3&"3,3&"4,3)400 "1,3&"2,3&"3,3&"4,3*"g400

3.#dentikasi +ungsi b-ektif

in100"1,1&100"1,2&120"1,3&120"2,1&100"2,2&100"2,3&100"3,1&110"3,2&120"

rimal

asis

100 100 120 120 100 100

"1,1 "1,2 "1,3 "2,1 "2,2 "2,3

0 "a 1 1 1 0 0 0

0 "b 1 1 1 0 0 0

0 "( 1 1 1 0 0 0

0 "d 1 1 1 0 0 0

1000 "/ 1 0 0 1 0 0

1000 "i 0 1 0 0 1 0

1000 "- 0 0 1 0 0 1

( ro *00 *00 *0 *0 *00 *00

"1,1&"1,2

"2,1&"2,2

"3,1&"3,2

"4,1&"4,2

"1,1&"2,1

"1,2&"2,2

"1,3&"2,3


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100 "1,1 1 1 1 0 0 0

0 "b 0 0 0 0 0 0

0 "( 0 0 0 0 0 0

0 "d 0 0 0 0 0 0

1000 "/ 0 *1 *1 1 0 0

1000 "i 0 1 0 0 1 0

1000 "- 0 0 1 0 0 1

( ro 0 0 20 *0 *00 *00

100 "1,1 1 1 1 0 0 0

0 "b 0 0 0 0 0 0

0 "( 0 0 0 0 0 0

0 "d 0 0 0 0 0 0

1000 "/ 0 *1 *1 1 0 0

100 "2,2 0 1 0 0 1 0

1000 "- 0 0 1 0 0 1

( ro 0 00 20 *0 0 *00

100 "1,1 1 1 1 0 0 0

0 "b 0 0 0 0 0 0

0 "( 0 0 0 0 0 0

0 "d 0 0 0 0 0 0

1000 "/ 0 *1 *1 1 0 0

100 "2,2 0 1 0 0 1 0

100 "2,3 0 0 1 0 0 1

( ro 0 00 20 *0 0 0

100 "1,1 1 1 1 0 0 0

0 "b 0 0 0 0 0 0

0 "( 0 0 0 0 0 0

0 "d 0 0 0 0 0 0

100 "3,1 0 *1 *1 1 0 0

100 "2,2 0 1 0 0 1 0

100 "2,3 0 0 1 0 0 1

( ro 0 0 20 20 0 0

Dual "1,1 "b "( "d "3,1 "2,2 "2,3

1 0 0 0 0 0 0

1 1 0 0 0 0 0

1 0 1 0 0 0 0

1 0 0 1 0 0 0

1 0 0 0 1 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

(b 100 0 0 0 100 100 100

1 0 0 0 0 0 0

*1 1 0 0 0 0 0

*1 0 1 0 0 0 0

*1 0 0 1 0 0 0


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*1 0 0 0 1 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1


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,3&100"4,1&110"4,2&120"4,3&m"/&m"i&m"-

100 110 120 100 110 120 0 0

"3,1 "3,2 "3,3 "4,1 "4,2 "4,3 "a "b

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 1 0 0 0 0

0 1 0 0 1 0 0 0

0 0 1 0 0 1 0 0

*00 *0 *0 *00 *0 *0 0 0

"1,3&xa150

"2,3&xb450

"3,3&xc300

"4,3&xd300

"3,1&"4,1*"e&xh400

"3,2&"4,2*"f&xi400

"3,3&"4,3*"g&xj400


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0 0 0 0 0 0 1 0

0 0 0 0 0 0 *1 1

0 0 0 0 0 0 *1 0

0 0 0 0 0 0 *1 0

1 0 0 1 0 0 *1 0

0 1 0 0 1 0 0 0

0 0 1 0 0 1 0 0

*00 *0 *0 *00 *0 *0 00 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 *1 1

0 0 0 0 0 0 *1 0

0 0 0 0 0 0 *1 0

1 0 0 1 0 0 *1 0

0 1 0 0 1 0 0 0

0 0 1 0 0 1 0 0

*00 10 *0 *00 10 *0 00 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 *1 1

0 0 0 0 0 0 *1 0

0 0 0 0 0 0 *1 0

1 0 0 1 0 0 *1 0

0 1 0 0 1 0 0 0

0 0 1 0 0 1 0 0

*00 10 20 *00 10 20 00 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 *1 1

0 0 0 0 0 0 *1 0

0 0 0 0 0 0 *1 0

1 0 0 1 0 0 *1 0

0 1 0 0 1 0 0 0

0 0 1 0 0 1 0 0

0 10 20 0 10 20 0 0

6arga beli gudang7ton 6arga -ual dipasar

0 0 0 0 100 100 100

150 450 300 300 400 400 400

0 0 0 0 40000 40000 40000


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0 0 0 0 0 1000 1000 1000

"( "d "e "f "g "/ "i "-

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 *1 0 0 1 0 0

0 0 0 *1 0 0 1 0

0 0 0 0 *1 0 0 1

0 0 1000 1000 1000 0 0 0


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0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 *1 0 0 1 0 0

0 0 0 *1 0 0 1 0

0 0 0 0 *1 0 0 1

0 0 1000 1000 1000 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 *1 0 0 1 0 0

0 0 0 *1 0 0 1 0

0 0 0 0 *1 0 0 1

0 0 1000 100 1000 0 00 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 *1 0 0 1 0 0

0 0 0 *1 0 0 1 0

0 0 0 0 *1 0 0 1

0 0 1000 100 100 0 00 00

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 *1 0 0 1 0 0

0 0 0 *1 0 0 1 0

0 0 0 0 *1 0 0 1

0 0 100 100 100 00 00 00

120000


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konstanta ratio

150 150

450 450

300 300

300 300

400 400

4008

4008

1200000 *00


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1508

3008

1508

1508

2508

400 400

4008

1095000 *00

1508

3008

1508

1508

2508

4008

400 400

:05000 *00

1508

3008

1508

1508

250 250

4008

4008

345000 *33.3333 *00

1508

3008

1508

1508

250 250

4008

4008

120000 8 0


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produk

$umber Da!a

laba7unitteknis tenaga ker-a administrasi

1 3 1 2 9

2 1 2 2 9

3 2 2 1 :

tersedia 400 400 40

1.#dentikasi ;ariabel

"1ban!akn!a -am teknis digunakan

"2ban!akn!a -am tenaga ker-a digunakan

"3 ban!akn!a -am administrasi digunakan

2.#dentikasi %endala $tandarisasi & %anonikal

3"1&"2&2"3'400 3"1&"2&2"3&"4400

"1&2"2&2"3'400 "1&2"2&2"3&"54002"1&2"2&"3'40 2"1&2"2&"3&"940

3.#dentikasi +ungsi b-ektif

ma"9"1&9"2&:"3

ma"1440

sumber da!a penggunaan tersedia eban %er-a


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?.@eknis 450 400 112.5

@.%er-a 400 400 100


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ma" >9"1&9"2&:"3

kendala baru standarisasi non*%anonikal

3"1&"2&2"3&"4400 3"1&"2&2"3&"4400 3"1&"2&2"3&

"1&2"2&2"3&"5400 "1&2"2&2"3&"5400 "1&2"2&2"3&

2"1&2"2&"3&"940 2"1&2"2&"3&"940 2"1&2"2&"3&

"1)100 "1*":100 *X1&X:*100

asis9 9 :

"1 "2 "3

: "4 3 1 2

9 "5 1 2 2

9 "9 2 2 1

0 ": *1 0 0

( ro *33 *25 *25

ratio 33: "4 0 1 2

9 "5 0 2 2

9 "9 0 2 1

9 "1 1 0 0

( ro 0 *25 *25

solusi optimal

="2 0= "30 =A4:0


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0 0 0%onstanta Basio

"4 "5 "9

1 0 0 450 225

0 1 0 400 200

0 0 1 40 40

0 0 0

0.5 0 0 225 450

*1 1 0 *50 *50

*0.5 0 1 255 1:0

*3.5 0 0

1 *0.5 0 250 100

*1 1 0 *50 8

1 *1.5 1 330 4.25:1425:

*1 *2.5 0

27 : 47 : * 57 : 14.25:1425:

* 37 : 17 : 47 : 13.5:1425:1

27 : * 37 : 27 : 4.25:1425:

*1 17 : *2 27 : * 17 : 14: 17 :

ketC


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bottlene(k

bottlene(k

bottlene(k

optimal hasil point (a)

i optimal hasil point (a)

! c!"(#$"*'$4'c1$%)!

uk 4, +ang butuh % jam la+anan teknis, 1 jam tenaga kerja, dan 3 jam a

0 0 0 %onstanta

"4 "5 "9 ":

1 0 0 2 400

0 1 0 1 400

0 0 1 3 40

0 0 0

1 *1 17 3 2 190

0 1 * 17 3 0 240

0 0 17 3 1 190

0 0 *3 0

1 *1 17 5 27 5 2 112

0 37 5 * 17 5 0 144

0 * 17 5 27 5 1 112

0 *2 27 5 *2 17 5 0 2019

! unit atau lebih tentukan solusi

! c!"(c3$"*'$4'$%)!


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4400

5400 ))))gunakan dual simple"

940

0 0 0 0%onstanta

"4 "5 "9 ":

1 0 0 0 400

0 1 0 0 400

0 0 1 0 40

0 0 0 1 *100

*: *9 *9 0

01 0 0 3 100

0 1 0 1 300

0 0 1 2 20

0 0 0 *1 100

*: *9 *9 *33 4:0


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minsitrasi, dan produk dapat memberikan keuntungan perunit sebesar &unit

Basio

200

400

190

40

144

40


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diambil dari 2a optimal

asis9 9 : 0 0

"1 "2 "3 "4 "5

: "3 0 0 1 27 : 47 :

9 "2 0 1 0 * 37 : 17 :

9 "1 1 0 0 27 : * 37 : ro 0 0 0 *1 17 : *2 27 :

persamaan Gomor! 1

0E"1&1E"2&0"3&*37:E"4&17:E"5&47:E"913 47:

0&0E"1&1&0E"2&0&0E"3&*1&47:E"4&0&17:E"5&0&47:E"913&47:E

ma"9"1&9"2&:"3

asis9 9 : 0 0

"1 "2 "3 "4 "5

: "3 0 0 1 27 : 47 :

9 "2 0 1 0 * 37 : 17 :

9 "1 1 0 0 27 : * 37 :

0 ": 0 0 0 * 47 : * 17 :

ro 0 0 0 *1 17 : *2 27 :

ratio 2 19

: "3 0 0 1 1 37 4

9 "2 0 1 0 *1 0

9 "1 1 0 0 0 * 17 2

0 ": *0 *0 *0 1 17 4

ro 0 0 0 *1 *2 17 4

ratio

X11=X2113= X315 =A14:

0"1&0"2&0"3&47:"4&17:"5&47:"9F47:

0"1&0"2&0"3&47:"4&17:"5&47:"9*":47:

0"1&0"2&0"3*47:"4*17:"5*47:"9&x#*47:


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0%onstanta Basio

"9 pe(a/an

* 57 : 14 27 : 27:

47 : 13 47 : 47:

27 : 4 27 : 27:* 17 : 14: 17 : 17:

0 0%onstanta ratio

"9 ": pe(a/an

* 57 : 0 14 27 : 27:

47 : 0 13 47 : 47:

27 : 0 4 27 : 27:

* 47 : 1 * 47 : *47:

* 17 : 0 14: 17 : 17:

17 4

0 *1 17 4 15

0 1 13

0 17 2 4

1 *1 37 4 1

0 * 17 4 14:


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simple" biasa berfokus pada ratio minus dan ( ro

dual simple" berfokus pada ratio !ang berkebalikan--lihat ko


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nstanta terminus dan kendala minus


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+ormulasi standarisasi

"1F50 "1F50

"2F100 "2F100

"3F100 "3F100

"1&"2&"3F1900 "1&"2&"3F1900

"1&2"2&2"30 "1&2"2&2"30

research operation

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